We have previously presented evidence for a varying fine-structure constant , \alpha , in two independent samples of Keck/HIRES QSO absorption spectra .
Here we present a detailed many-multiplet analysis of a third Keck/HIRES sample containing 78 absorption systems .
We also re-analyse the previous samples , providing a total of 128 absorption systems over the redshift range 0.2 < z _ { abs } < 3.7 .
The results , with raw statistical errors , indicate a smaller weighted mean \alpha in the absorption clouds : \Delta \alpha / \alpha = ( -0.574 \pm 0.102 ) \times 10 ^ { -5 } .
All three samples separately yield consistent and significant values of \Delta \alpha / \alpha .
The analyses of low- z 
( i.e . z _ { abs } < 1.8 ) and high- z systems rely on different ions and transitions with very different dependencies on \alpha , yet they also give consistent results .
We identify an additional source of random error in 22 high- z systems characterized by transitions with a large dynamic range in apparent optical depth .
Increasing the statistical errors on \Delta \alpha / \alpha 
for these systems gives our fiducial result , a weighted mean \Delta \alpha / \alpha = ( -0.543 \pm 0.116 ) \times 10 ^ { -5 } , representing 4.7 \sigma evidence for a varying \alpha .
Assuming that \Delta \alpha / \alpha = 0 at z _ { abs } = 0 , the data marginally prefer a linear increase in \alpha with time rather than a constant offset from the laboratory value : \dot { \alpha } / \alpha = ( 6.40 \pm 1.35 ) \times 10 ^ { -16 } { yr } ^ { -1 } .
The two-point correlation function for \alpha 
is consistent with zero over 0.2–13 Gpc comoving scales and the angular distribution of \Delta \alpha / \alpha shows no significant dipolar anisotropy .
We therefore have no evidence for spatial variations in \Delta \alpha / \alpha .

We extend our previous searches for possible systematic errors , giving detailed analyses of potential kinematic effects , line blending , wavelength miscalibration , spectrograph temperature variations , atmospheric dispersion and isotopic/hyperfine structure effects .
The latter two are potentially the most significant .
However , overall , known systematic errors do not explain the results .
Future many-multiplet analyses of independent QSO spectra from different telescopes and spectrographs will provide a now crucial check on our Keck/HIRES results .